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1

Korovkin-type approximation by operators in Riesz spaces via power series method

Chil Elmiloud, Assili Marwa

Demonstratio Mathematica

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2019

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Vol. 52, nr 1

490--495

EN

In this paper we prove an Ozguç, Yurdakadim and Taş version of the Korovkin-type approximation by operators in the sense of the power series method. That is, we try to extend the Korovkin approximation theorems, obtained by Ozguç and Taş in 2016, and Taş and Yurdakadim in 2017, for concrete classes of Banach spaces to the class of Riesz spaces. Some applications are presented.

2

Ordered vector valued double sequence spaces

Dey R., Das N. R., Tripathy B. C.

Fasciculi Mathematici

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2015

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Nr 55

29--34

EN

In this paper we have introduced an order relation on convergent double sequences and have constructed an ordered vector space, Riesz space, order complete vector space in case of double sequences. We have verified the Archimedean property.

3

On the Riesz space properties of the space of real statistically convergent sequences

Sencimen T. T, Pehlivan S

Journal of Applied Analysis

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2013

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Vol. 19, nr 1

31--39

EN

In this paper, we investigate some Riesz space (vector lattice) properties of the space of real statistically convergent sequences. We prove that this space is an order dense Riesz subspace of the linear space of all real sequences, but it is not an ideal.

4

A characterization of u-iniformly completeness of Riesz spaces in terms of statistical u-uniformly pre-completeness

Ercan Z.

Demonstratio Mathematica

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2009

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Vol. 42, nr 2

381-385

EN

In this paper we introduce statistically u-uniformly convergent sequences in Riesz spaces (vector lattices) and then we give a characterization of u-uniformly completeness of Riesz spaces.

5

Order properties of the space of A-linear operators

Turan B.

Demonstratio Mathematica

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2006

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Vol. 39, nr 2

429-438

EN

Let A be an f-algebra with unit and L, M be two topologically full f-modules on A. We prove that the space of A-linear operators Lb(L, M; A) is a Riesz space and we study the order properties of the adjoint operator from Lb(L, M; A) to Lb(M~, L~; (A)^n). The main result given here describes the centre of the space of Lb{L, M; A).

6

Exhaustivity in topologicai Riesz spaces with the principal projection property

Muller K.

Bulletin of the Polish Academy of Sciences. Mathematics

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2006

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Vol. 54, no 1

53-62

EN

Exhaustive and uniformly exhaustive elements are studied in the setting of locally solid topological Riesz spaces with the principal projection property. We study the structure of the order interval [O, χ] when x is an exhaustive element and the structure of the solid hull of a set of uniformly exhaustive elements.